Question

the theoretical probability of an event is the number of ways an event can occur divided by the total number of possible outcomes:
$p(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}$
what is the theoretical probability of selecting a king from a standard deck of 52 playing cards?
options: 1/13, 1/4, 4/13, 4

Explanation:

Step1: Identify favorable and total outcomes

In a standard deck, number of kings (favorable) = 4, total cards = 52.

Step2: Apply probability formula

Using \( P(\text{king}) = \frac{\text{number of kings}}{\text{total number of cards}} = \frac{4}{52} \).

Step3: Simplify the fraction

Simplify \( \frac{4}{52} \) by dividing numerator and denominator by 4: \( \frac{4\div4}{52\div4} = \frac{1}{13} \).

Answer:

\( \frac{1}{13} \) (corresponding to the option "1/13")